Non-linear waves in chromatography .3. Multicomponent Langmuir and Langmuir-like systems

This third instalment on non-linear waves examines in detail the chromatographic behavior of multicomponent systems whose sorption equilibria are uniformly competitive and without selectivity reversals. This very common class includes systems with multicomponent Langmuir isotherms, but is not restricted to them. An examination of particle velocities and wave velocities leads to a set of rules for what may and may not happen in a column if sorption equilibrium is of this type. As an example, all qualitative features of frontal analysis are deduced without calculation. The arguments also illustrate how, more generally, wave theory can be used to deduce chromatographic behavior from given equilibrium properties. In addition, an easy-to-use mathematical procedure is presented with which column responses in systems with Langmuir sorption isotherms can be calculated. The procedure is based on a transformation of the concentration variables. Compositions of plateau zones between waves, wave velocities, and sharpening criteria are obtained as simple algebraic expressions or conditions in terms of the values of the new variables in only the initial and entering fluids. The new variables are easily transformed back into concentrations where this is desired. Three fully calculated examples of five-component frontal analysis, separation of a three-component mixture by displacement development, and two-component elution from an overloaded column show how analytical solutions can be obtained for many cases of practical interest. As in Part II, the assumptions of ideal chromatography are taken for granted.